Econ assignment

ECON 3551 Managerial Economics & Business Strategy

Midterm Revision Spring 2018

Instructions:

 This is a required assignment for those who achieved 10 points or less on Problems 1-4 on the midterm. Not submitting it results in a WU (unauthorized withdrawal) grade for the course. For others, who scored 11 points or above on the problem section of the final, it is recommended.

 Submit the answers in the provided space, as well as your work on separate pages (typed or handwritten) in hardcopy on Thursday, 5/17, either in class or under my office door by 6 pm. No late submissions will be accepted.

 You may seek help from classmates or tutors, but write up your solutions independently.

P1 A marketing analyst has estimated a firm’s demand function to be 𝑄 = 40 − 2𝑃 + 20𝑋, where X is an indicator for whether the economy is in a boom (X = 1) or recession (X = 0). Marginal cost of producing the good is 10.

i) Write down the inverse demand, i.e. P as a function of Q and X. ii) Write down the marginal revenue function during a boom as a function of Q. iii) What is the firm’s optimal price during a boom? iv) Write down the marginal revenue function during a recession as a function of Q. v) What is the firm’s optimal price during a recession?

P2 A snack company’s data analysts have estimated the following elasticities for sales of the firm’s products. Price elasticity is –2.5. Income elasticity is –0.8. Cross-price elasticity with chocolate bars is +0.5. Advertising elasticity is +0.8. Marginal cost is $6.

i) What is the optimal profit margin (P – MC)/P in percent? ii) What is the optimal price? iii) If the price of chocolate bars increases by 10%, by how much do the sales of the company change? (Pay attention to the right sign.) iv) If the price of chocolate bars increases by 10%, and consumer incomes decrease by 5% at the same time, by how much do the sales of the company change? (Pay attention to the right sign.) v) If the firm wants to achieve 20% sales growth, by how much does it need to increase its advertising expenditure?

P3 Consider the cost function 𝐶 = 40 + 3𝑄 − 2𝑄 + 𝑄 .

i) At Q = 4, what is the firm’s average fixed cost? ii) At Q = 4, what is the firm’s marginal cost? iii) If the firm optimally produces Q = 4, and 𝑃 = 35 − 𝑎𝑄, what does a have to be? iv) Which Q minimizes the firm’s average variable cost? v) What is the firm’s minimum average variable cost?

P4 A firm makes two goods, A and B, with production functions 𝑄 = 2𝐾 (𝐿 ) and 𝑄 = 16𝐾 +4𝐿 . The firm has a fixed total supply of capital of 1 unit, and it can hire labor at PL = $10 for the first 5 hours, and for the overtime rate of PL = $20 after that, up to 10 hours. Output prices are PA = $2 and PB = $1.

i) So that capital’s marginal revenue product is equal for A and B, what must LA be? ii) How much labor should the firm hire to work on B? iii) If KA = 1, what is the overall revenue from QA and QB? iv) If KA = 0, what is the overall revenue from QA and QB? v) What is the profit contribution (revenue minus labor cost)?

ANSWER SPACE

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Problems

P1 i)

P1 ii)

P1 iii)

P1 iv)

P1 v)

P2 i)

P2 ii)

P2 iii)

P2 iv)

P2 v)

P3 i)

P3 ii)

P3 iii)

P3 iv)

P3 v)

P4 i)

P4 ii)

P4 iii)

P4 iv)

P4 v)