markets practice problems

8/10/2019 Markets Practice Problems

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Microeconomics I

Assignment 2

Due on: September 15, 2014 (before 02:30 PM)

To be submitted to Mr. Manhar (TA)

1. Assume that all firms in a perfectly competitive industry have an identical costfunction given by C(w1, w2, y) = y

2

(w1w2) + 8, where w1 and w2 are the factor

prices and y is a firms output. The market demand function in this industry is

D(p) = 40p, where pis the price of output.

(a) Find the unconditional factor demands and the supply of each firm in this

industry.

(b) Suppose the factor prices are w1 = 4 and w2 = 25, and the number of firms isequal to 30. Find the short run equilibrium price in this industry.

(c) Suppose that the factor prices are w1 = 4 and w2 = 1. Find the long run

equilibrium price and the number of firms in the industry.

(d) If the government imposes a per unit sales taxt. How will the long run equilib-

rium number of firms change due to imposition of sales tax? Will there be any

dead-weight loss due to sales tax in the long run?

(3+3) + 3 + (3+3) + 5=20


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IGIDR 2014 Microeconomics I, Assignment 2

2. Consider a competitive firm which has the following production function.

y=f(h(w)l),

where l and w refer to hours of labour and the hourly wage rate, respectively. The

production function f(.) is increasing and strictly concave in h(w)l > 0, which is

labour measured in efficiency units: f(0) = 0. Further, the efficiency functionh(w)

is also increasing and strictly concave in w, but w must exceed w for h(w) to be

positive: at all w w, h(w) = 0.

The firm has no other input than labour. At a given product pricep, it can freely

choose w and l to maximize profits subject to the constraint that the chosen wage

rate cannot be less than the market wage rate wm, which is determined in the labour

market. No worker will join the firm, if the firm offers w < wm.

(a) Derive the firms labour demand function ld(wm, p) taking into account that it

will try to optimize on the wage rate as well.

(b) Write the product supply curve as well.

(c) Draw the labour demand and output supply curves separately and show how

these curves behave with respect to important shift parameters.

5+2+(4+4)=15

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3. A farmer has a fixed plot of land L that can be used to produce two crops, food

crop y1 and fodder y2, which can be sold in the market at fixed prices p1 and p2,

respectively. The production technologies of the two crops are given as follows.

y1 = F(L1) and y2=F(L2),

where F(.) and G(.) are both increasing and strictly concave. Li is the plot of land

devoted to the production of the ith crop. Since the total amount of land is fixed, it

must hold that L1+ L2 = L.

(a) Can you tell us what all combinations ofy1 and y2 the farmer can produce, if

no land remains uncultivated? Please show that in a graph as well.

(b) Suppose the farmer does not have to bear any cost of production, Now, if he

wants to maximize profit by producing the two crops, which equations will

determine his choices ofL1and L2? Discuss, how the allocation ofLwill depend

on the prices of and technologies for the two crops. For the sake of comparison

you should also consider the case ofF(.) and G(.) being identical.

(c) If a real-estate developer acquires some land from the farmer, how will his choice

ofL1 and L2 be affected?

2+(2+4)+2=10

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4. Consider the case of a public sector firm. The government requires the firm to hireno

less than30 workers (l). The firm is of course free to hire any amount of capital (k)

it wishes. The prices of labour and capital are w andr, respectively. The production

function of the firm is

y= Min {10l, 15k}.

(a) Derive the firms cost function.

(b) Can you define and identify an overmanning problem in this context?

(c) What is the excess cost due to overmanning?

(d) Now suppose the government slightly changes its policy. It allows the firm to

pay different wage rates at different levels of output, but still the firm is required

to hire at least 30 workers. If the firm wants to eliminate the excess cost, how

will it adjust the wage rate?

2+5+3+5=15

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markets practice problems

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