UNIVERSITY OF CALGARY
DEPARTMENT OF ECONOMICS
ECONOMICS 301
Assignment 2
Wojciech (Victor) Fulmyk Winter 2023
This assignment is due on D2L on Wednesday, April 12, 2023, at 11:59pm. You
submission has to be a single .pdf file
Note: Throughout the assignment assume prices and quantities are perfectly
divisible. If necessary, round your answers to 2 decimal points.
1. Suppose that you have some information about a firmâ€™s variable and fixed costs in the
short-run. Suppose a firmâ€™s variable costs are Cv(y) = 20
âˆš
y + 4wy2, where w is the
price of the firmâ€™s variable factor. Moreover, suppose the firmâ€™s fixed costs are F = 20.
(a) Solve for the firmâ€™s marginal cost function.
(b) Solve for the firmâ€™s average cost, average variable cost, and average fixed cost.
(c) For the rest of the question, assume w = 1. Solve for the firmâ€™s shutdown
price.
(d) Suppose the price of the output good is $10. At this price, does the firm operate?
If so, what are the firmâ€™s profits?
(e) Suppose the price of the output good is $14. At this price, does the firm operate?
If so, what are the firmâ€™s profits?
(f) Suppose the price of the output good is $18. At this price, does the firm operate?
If so, what are the firmâ€™s profits?
2. Suppose you are analyzing a particular market. All consumers in this market have
the utility function U(y1, y2) = y2 + 10y1 âˆ’ y21/2. Suppose that there are many firms
producing good 1, and that each of these firms has the production function y1 =
2L0.5 + 4K0.5. Assume good 2 is a composite good with price p2 = 1.
(a) Derive a consumerâ€™s Marshallian demand for good 1. Assume all consumers can
always afford good 1.
(b) For the rest of this question, suppose there are 5 consumers in total in
the market. What is the aggregate demand for good 1?
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ECON 301 Assignment 2 Winter 2023
(c) What is the price elasticity of demand for prices p1 = 1, p1 = 5, and p1 = 10?
(d) Find the conditional factor demands for L and K for a typical firm producing
good 1.
(e) Suppose the government forces all firms operating in the market to purchase a
$20 operating license. What is the cost function of a firm?
(f) For the rest of the question, assume that all input prices are equal to 1.
What is the supply curve of a firm in this market? (Note: Assume the long-run
case, that is, that the supply is zero if profits are negative.)
(g) If there was only one firm supplying the market, what would the equili
ium price
and quantity be? (Note: do not assume any complicated strategic behaviour. Fo
instance, do not assume that this is a monopoly and that this firm would act
like a monopolist; rather, view this as a short-run case where the firm behaves
according to the supply curve you identified in the previous part.)
(h) Calculate the profits for this individual firm supplying the market.
(i) Assume firms have no ba
iers to entry or exit. Moreover, assume there are no
estrictions on the number of operating licenses issued. In the long-run, how many
firms will exist in this market? What will the equili
ium price and quantity be?
(j) Compare the short-run, single firm equili
ium to the long-run equili
ium. What
are the prices, quantities and average costs of production under each equili
ium?
What is the producer and consumer surplus under each equili
ium?
3. Suppose a consumerâ€™s utility function for goods 1 and 2 is u(y1, y2) = min(10y1, 2y2).
Suppose a firm producing good 1 has the production function f(x1, x2) = x2+x1+x2x1.
Suppose the price of factor 2 is w2 = 1, and let w1 denote price of input 1. (Assume
input 1 is labour and input 2 is capital).
(a) Derive the consumerâ€™s Marshallian demand for goods 1 and 2.
(b) Derive the consumerâ€™s Hicksian demand for goods 1 and 2.
(c) Suppose the firm is required to produce 8 units of output. For which values of w1
would a cost-minimizing firm use
i. only labour?
ii. only capital?
iii. both capital and labour?
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ECON 301 Assignment 2 Winter 2023
4. Suppose a consumerâ€™s utility function for goods 1 and 2 is u(y1, y2) = 4y1 + 10y2.
Suppose a firm producing good 1 has the production function f(x) = 9/xâˆ’2/3, where
x is the amount of some input used by the firm to produce output y1.
(a) Derive the consumerâ€™s Marshallian demand for goods 1 and 2.
(b) Derive the consumerâ€™s Hicksian demand for goods 1 and 2.
(c) Find the marginal product of input x.
(d) Suppose that the cost of input x is w = 9 and that the output price is p = 3.
Draw the production function for this firm. Also, draw the isoprofit lines whose
vertical intercepts are the points (0,12), (0,8), and (0,4). What is the slope of
these isoprofit lines?
(e) Suppose that the cost of input x is w = 9 and that the price of output is p = 3.
How many units of input x will the firm choose to hire? How many units of
output will the firm choose to produce? If there are no other costs, what would
the firmâ€™s total profit be?
(f) Now, suppose that the cost of input x drops to w = 6 and that the output price
emains at p = 3. Will the firm choose to increase itâ€™s output at the new price?
What will the firmâ€™s new output level be? How many units of the input will the
firm choose to hire now? If there are no other costs, what is the firmâ€™s total profit?
5. Define all of the following concepts in your own words and describe the relationship
etween all concepts on the same line.
(a) Isoquant, Technical rate of substitution, and marginal product.
(b) Returns to scale and economies of scale.
(c) Cost function, conditional factor demands, and factor demands.
(d) Marginal cost, Average cost, average variable cost, and average fixed cost.
6. If we price all inputs at their opportunity cost, then why do we say that the payment
to some inputs is an economic rent? What is the difference between an economic rent
and any other opportunity cost?
7. Suppose a firm has a production function that is strictly convex and well-behaved.
Suppose the firm has just two inputs into the production process. Additionally, suppose
the firm is operating where the absolute value of its technical rate of subsititution is
less than the input price ratio (w1/w2), where w1 is the price of input 1 and w2 is the
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ECON 301 Assignment 2 Winter 2023
price of input 2. How can this firm increase its output without changing the amount
it spends on its inputs? Additionally, provide an argument for why a firm operating
where the absolute value of its technical rate of subsititution is less than (w1/w2)
cannot be profit maximizing.
8. Suppose the market for Widgets is perfectly competitive market. Suppose all con-
sumers in the marhet are identical and have a utility function betweenWidgets (W ) and
and the composite good (CG) defined by U(W,CG) = W 6CG2. Suppose that the ag-
gregate demand and industry supply curves for Widgets are given by QD = 2000âˆ’20P
and QS = 60P . Suppose the government provides a subsidy of $20 per Widget to all
sellers in the market.
(a) Find the equili
ium quantity of Widgets demanded and supplied; find the equilib-
ium market price paid by buyers; find the equili
ium after-subsidy price received
y firms.
(b) Suppose each consumer in the market has a budget m = 100. How many Widgets
will each consumer consume in equili
ium with the subsidy? In order for all
produced Widgets to be purchased, how many identical consumers would we
need?
(c) Find consumersâ€™ surplus and producersâ€™ surplus in the absence of the subsidy.
What is the net economic benefit in the absence of a subsidy?
(d) Find consumersâ€™ surplus and producersâ€™ surplus in the presence of the subsidy.
What is the impact of the subsidy on the government budget? What is the net
economic benefit under the subsidy program?
(e) Does the subsidy result in a deadweight loss? If so, how much is it?
9. Suppose we have a competitive industry with many firms, all of which have the cost
function c(y) = y2 + 1 when y > 0 and c(0) = 0. Suppose that. initially, aggregate
demand is D(p) = 84âˆ’p. Note that the number of firms has to be an interger amount,
ut that prices and quantities do not have to be intergers.
(a) Solve for an individual firmâ€™s supply curve? If there are n firms in the market,
what is the market supply curve?
(b) In the long-run, what is the minimum price at which this product will be supplied?
(c) What is the equili
ium number of firms in the market?
(d) What is the equili
ium price? What is the output of every firm in the market?
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ECON 301 Assignment 2 Winter 2023
(e) What is the aggregate output of all firms in the market at the equili
ium?
(f) Now, suppose that the market demand curve shifts to D(p) = 84.5âˆ’p. What will
e the equili
ium number of firms be now? What will be the equili
ium price?
What will be the output of each firm? What will be the profit of each firm in the
market?
(g) Now, suppose that the market demand curve shifts to D(p) = 85âˆ’ p. What will
e the equili
ium number of firms? What will be the equili
ium price? What
will be the output of each firm in the market? What will be the profit of each
firm in the market?
10. True or False. For full marks, you MUST explain your answer!
(a) Suppose you have a firm that uses a production process with two inputs. Suppose
that in the short run, input 1 is variable and input 2 is fixed. If the price of
the input 2 goes up, the firmâ€™s short-run average variable cost, average cost, and
marginal cost curves will all shift upward.
(b) Suppose you have a firm that uses a production process with two inputs. Suppose
that in the short run, input 1 is variable and input 2 is fixed. If the price of
the input 1 goes up, the firmâ€™s short-run average variable cost, average cost, and
marginal cost curves will all be unaffected.
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