MICROECONOMICS 2 ASSIGNMENT
DUE FRIDAY 23 JULY
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1. demand and supply
(a) Suppose widegts have a price elasticiyt of demand equal to -1.95
and a cross elasticitiy of demand equal to 2 with dundles. What
are the pricing options for a firm that sells widgets? Explain. (5
marks)
(b) If the quantity demand for apples is given by:
QD = 300 − 2.55pA + 7.62pB + 0.75Y
(1)
if pA = 90 cents, pB = 50cents and QD = 860.
Calculate and interpret the income elasticity of demand for apples.
(3 marks)
(c) Make a use of calculus to prove that the price elasticity of demand
is a constant ε everywhere along the demand curve whose function
is Q = Apε , where A is a positive constant and p is the market
price. (4 marks)
2. A consumers has a choice between two products, clothes and food. If
food is a giffen good and clothes are a normal good:
(a) Use consumer theory to derive the demand curve of clothes. (4
marks)
(put clothes on the horizontal axis in this part)
(b) Use diagrams to explain the change in quantity of food consumed
when its price decreases. (5 marks)
(put food on the horizontal axis in this part - explain both the
income and sustitution effects.)
3. We assumes a firms production is determined on two inputs, capital(K)
and labour(L).
(a) Explain the following terms using a diagram. (9 marks)
i. A Cobb-Douglas production function
ii. Isoquants and Isocosts
iii. The long-run equilibrium
(b) Suppose that a firms out put is given by:
q = αLK 2
Where α is a productivity factor.
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(2)
i. Specify the marginal products of labour and capital. (4 marks)
ii. If the cost function is C = wL + rK. Specify the quanitites
of capital and Labour that minimize costs. (6 marks)
4. The structure of a market is dertermined by certain characteristics such
as the number of buys and sellers, long-run profits, nature of demand
curve, possibilityof collusion e.t.c.
(a) Use the characteristics of a perfectly competitive market to explain
why the demand curve for a firm in perfectly competitive market
is perfectly elastic. (marks 3)
(b) Mathematically prove that for an market structure, the profit
maximizing level of output is obtained at the point where the
marginal cost is equal to marginal revenue i.e. M C = M R. (3
marks)
(c) if T C = 3 + Q2 and demand is P = 3 − 21 Q.
Calculate the firm’s total profit. (4 marks)
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