Question

Suppose that a firm's production function is q = 5x0.5 in the short run, where there are fixed costs of $2,000, and x is the variable input whose cost is S1250 per unit. What is the total cost of producing a level of output q? In other words, identify the total cost function C(q) The total cost of producing a level of output q is O A. C(g)-2,000. ca-2,000+ C(q) = 2,000 + Cla)= 800 O B. 25 % C. O D. 12502 8 10 12 14 16 18 20 25 Quantity Cla)-2,000 1250 25 Write down the equation for the supply curve

Answer 1

1) Production function: q = 5x0.5

Fixed Costs = $2000

Cost of variable input = $1250 per unit

Using the production function: x = q2/25

Cost: C(q) = 2000 + 1250*q2/25

C(q) = 2000 + 1250q2/25

The correct answer is option E)

2) For Supply function

Equate Price = Marginal Cost

Let price = p

Marginal Cost = dC(q)/dq

Marginal Cost = 100q

Supply Curve: P = 100q

The correct answer is option E)

3) Given price = $800

So using supply equation solve or q

We get q = 800/100 = 8 units.

4) So profit = 800*8 – 2000 – 50*64

Profit = $1200