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A firm in a perfectly competitive market has the following cost function:
C = 1/3q3 – 5q2 + 30q +10
If the market-clearing price is 6, obtain the profit maximising level of output.
OR
Given the demand function PD = 27 – Q 2 and supply function Ps = 2Q + 3. Assuming perfect
competition, find (i) the consumers’ surplus, (ii) the producers’ surplus.
Let X{1,3,5 and Y{2,4,6} Find, X U Y and the Cartesian Product of X and Y.
OR
Find the integral of (y2 -1) dx-2dy = 0
A monopolist faces the demand curve Q = 60-P/2. The cost function is C=Q2 . Find the output that maximises this monopolist’s profits. What are the prices at profits and that output? Find the elasticity of demand at the profit maximising output.
OR
A monopolist firm has the following total revenue and total cost functions:
R = -mQ2 + nQ ( m,n > 0)
C = aQ2 + bQ + c (a,b,c > 0)
Suppose that the government plans to levy an excise tax on the product of this firm and wishes to maximise the total tax revenue T from this source. What tax rate t ( rupees per unit of output) should the government choose?
Given the aggregate consumption function C = 0.9Y + 100(where C is aggregate consumption and Y is aggregate income)
(a) Find the marginal propensity to consume (MPC) and average propensity to consume (APC)
(b) Find the elasticity of consumption with respect to income, and show that it equals MPC/APC