ECON 408: Cost/Economies or Diseconomies of Scale

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Econ 408
Individual HW 1

1. A firm has a fixed production cost of $5000 and a constant marginal cost of production of $500 per unit produced.
a. What is the firm’s total cost function? Average cost?
2. The short-run cost function of a company is given by the equation TC  200  55q, where TC is the total cost and q is the total quantity of output, both measured 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 variable 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.
3. A computer company’s cost function, which relates its average cost of production AC to its cumulative output in thousands of computers Q and its plant size in terms of thousands of computers produced per year q (within the production range of 10,000 to 50,000 computers),
is given by
AC  10  0.1Q  0.3q.
a. Is there a learning curve effect?
b. Are there economies or diseconomies of scale?
c. During its existence, the firm has produced a total of 40,000 computers and is producing 10,000 computers this year. Next year it plans to increase production to 12,000 computers. Will its average cost of production increase or decrease? Explain.
4. A computer company produces hardware and software using the same plant and labor. The total cost of producing computer processing units H and software programs S is given by
TC  aH  bS  cHS
where a, b, and c are positive. Is this total cost function consistent with the presence of economies or diseconomies of scale? With economies or diseconomies of scope?

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