9. The short-run cost function of a company is given by the equation TC 200 + 53
ID: 1109768 • Letter: 9
Question
9. The short-run cost function of a company is given by the equation TC 200 + 534, where TC is the total cost and q is the total quantity of output, both meas- ured in thousands. a. What is the company's fixed cost? b. If the company produced 100,000 units of goods, what would be its average variable cost? c. What would be its marginal cost of production? d. What would be its average fixed cost? e. Suppose the company borrows money and expands its factory. Its fixed cost rises by $50,000, but its var- iable cost falls to $45,000 per 1000 units. The cost of interest (i) also enters into the equation. Each 1-point increase in the interest rate raises costs by $3000. Write the new cost equation.Explanation / Answer
A. The fixed cost of a company are the costs which do not change even when the production is 0. As per the equation when “q” is “0” , TC = 200 so fixes costs will be 200 or $200,000.
B. Avarage variable cost is Total variable cost divided by the production so if the company produces 100000 units the AVC will be calculated as :-
Q= 100 Variable cost is 55q so 5500 or $5500000 and AVC = 5500/100 so 55 or $55000.
C. Marginal cost (MC) is the change in total cost with the change in quantity but as the AVC is 55 (refer B) and constant so with constant AVC the MC will also be 55 or $55000.
D. Average fixes cost or AFC is the total cost divided by the quantity of output so in this case as q = 100
AFC = TFC/q As TFC is 200 (refer A) n q = 100 the AFC =$200/100 or $2 or $2000.
E.current fixed cost is 200 n it becomes 250 (as it is measured in thousands) (FC)
Current VAriable cost decreases from 55 to 45 (VC)
Fixed cost now also includes interest charges of 3(VCi) so the new equation becomes
TC =F.C. + VC*q +VC *i or TC = 250 + 45q + 3i
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