1. A new shop has opened and has the following production function:
Q=E0..25 K0.5
The price of output is $P, the wage rate is $w, and the rental rate of capital is $r. Hint, "as a function" means an equation that only has the parameters listed ie as a function of P, w, r, means no E or K in the right hand side of the equation.
a. Find the short-run labor demand equation as a function of P, w, r and K.
b. Find the long-run labor demand equation as a function of P, w, and r.
c. Find the long-run capital demand equation as a function of P, w, and r.
d. Find the long run production function as a function of P, w, r.
e. Find the long-run the elasticity. You do not need to type this answer or the mathematics. Leave a blank spot on your answer sheet and hand prepare your math.