Microeconomic Theory & The Investor Has Initial Wealth Cost & Profit Function - Economics Assignment Help

Assignment Task -         

1. In part a) derive the cost function, cwy (,) and b) profit function for the following  production function: 

1/3 1/4 

1 2 y xx = 

 c) What type of returns to scale does this production function exhibit?  d) Find the firm’s conditional demand for the two inputs.  

e) Suppose that input 2, 2 x is fixed in the short run. Derive the restricted cost function.  f) Can you derive the supply function ypw (, ). 

g) Derive the input demands from the profit function using Hotelling’s lemma. 

2. Consider the following “portfolio choice” problem. The investor has initial wealth w and  utility ux x ( ) = ln ( ). There is a safe asset (such as a US government bond) that has net real  return of zero. There is also a risky asset with a random net return that has only two possible  returns, R1 with probability q and R0 with probability 1− q. Let Z be the amount invested in the  risky asset, so that w − Z is invested in the safe asset. Note that w is her wealth. 

a). Find Z as a function of w. Does the investor put more or less of his portfolio into the risky  asset as her wealth increases? 

b). Another investor has the utility function ( ) x ux e− = − . How does her investment in the risky  asset change with wealth? 

′′ = − ′ for the two investors. How do  

c). Find the coefficients of absolute risk aversion ( ) ( ) ( ) 

u x  r xu x 

they depend on wealth? How does this account for the qualitative difference in the answers you  obtain in parts (a) and (b)? 

3) Suppose the inverse demand curve faced by a monopolist in market 1 is: 1 11 p q = − α β and inverse demand curve faced by a monopolist in market 2 is 2 22 p q = − α β with β β 1 2 > and has cost C q = δ where all parameters are positive , 

Note that total output 1 2 qq q = + 

a) Find the profit maximizing levels of output sold in each market. 

b) Specify the first and second order condition for profit maximization for this problem. c) What is the price elasticity of demand faced by this monopolist in each market? d) Which market faces the higher price for the good?

Extra Credit 

A per unit tax, t>0, is levied on the output of a monopoly. The monopolist faces demand : 

q p -a = where α >1 and has constant marginal costs. Show that the monopolist will  increase price by more than the amount of the per-unit tax.

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