The demand function for a product is q= 60

1. The demand function for a product is q= 60 over by p0.5

(a) Write the expression for the own price elasticity of demand ?(q).

(b) Compute the own price elasticity of demand ?(q) at q= 100.

(c) Generalize this example to compute own price elasticity of demand for the demand function given by q=A over p? where ? > 0.

2. The demand function for a product is p=220?0.5q.

(a) Write the expression for the total revenue function.

(b) Find the output quantity q? at which the total revenue function attains it’s maximum.

(c) Write the expression for the own price elasticity of demand ?(q).

(d) Compute the own price elasticity of demand ?(q?).

3. A two product firm faces the following demand and cost functions. Q1 =40?2P1?P2, Q2 =35?P1?P2, and C(Q1,Q2) = Q21 +2Q2 +10.

(a) Find the output levels Q?1 and Q?2 that satisfy the first order conditiond for maximum profit (use fracctions).

Hint: You may first determine the inverse demand functions (price as a function of quantity), P1(Q1,Q2) and P2(Q1,Q2) from the demand functions Q1(P1,P2), Q2(P1,P2).

(b) Compute the maximum profit.

4. Consider a competitive firm with the following profit function

where ? = R?C= PQ?wL?rK,

P= Price of the output Q= Output

L= Labor input

K= Capital input

w= wage rate for labor input

r= rental rate for capital input

and Q(K,L) = 16K1/4 L1/4.

(a)Find the input quantities K? and L? that satisfy the first order conditions for the profit maximization. Assume the parameter values P= 4, w= 1, and r= 1.

(b) Compute the profit maximizing output Q?.

(c) Compute the maximum profit ??.

(d) If the wage rate w changes to w= 2, determine the new L??.

(e) If the rental rate r changes to r= 2, determine the new L??.

(f) If the output price P changes to P= 16, determine the new L??.

Hint: All other parameters remain as in the original case in last three parts.

(g) Also compute the profit maximizing output Q?? and the maximum profit in each case ??? in each of the last three parts, i.e., (d)-(f).