Midterm Exam 2
ECO 301 – Spring 2013
Instructor: Michael Malcolm
Instructions: You can use any written materials you would like in completing this
exam, and a calculator.
Statement of academic honesty:
This exam entirely reflects my own work. I have not received assistance from
anyone or given assistance to anyone in completing this exam
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Consider a single-price monopoly that faces demand curve 𝑃 = 250 − 2𝑞 and which has total cost function 𝑇𝐶 = 𝐹 + 10𝑞, where 𝐹 is a fixed cost.
a. Find the profit-maximizing price and quantity for the monopolist.
b. What is the highest value that 𝐹 can take that still allows the firm to earn profits rather than losses?
At its optimal output level, a firm earns total revenue of $3500 but faces total costs of $7000.
a. Suppose that the firm has total fixed costs equal to $3000. What should this firm do in the short run?
In class, we assumed that the interest rates for borrowing and saving were equal. But, in reality, it is typically the case for consumers that the interest rate paid to borrow money exceeds the interest rate earned on savings.
Consider a simple two-period model where the consumer earns an income of $1500 in each period. If he saves, the interest rate he earns on his savings is 10%. But if he borrows money, he has to pay a 50% interest rate on the loan.
a. Where 𝐶1 and 𝐶2 represent the consumer’s spending in the first and second period, respectively, sketch the budget set below. Be sure to label the intercepts.
b. What is the optimal bundle if the consumer’s utility function is 𝑈 = min{𝐶1, 𝐶2}, i.e. when 𝐶1 and 𝐶2 are perfect complements? (Hint: Find the solution graphically)
This problem refers to the Edgeworth Box below. Albert and Beatrix trade Good X and Good Y. The initial allocation of the goods is X. Albert’s indifference curve through allocation X is labeled I_albert. Beatrix’ indifference curve though allocation X is labeled I_beatrix. The contract curve is drawn in. Five other potential allocations – A, B, C, D and E – are drawn in.
a. Which allocation(s) are Pareto improvements over allocation X?
b. Which allocation(s) are Pareto efficient?
c. Which allocation(s) are in the core?
d. Which allocation(s) would Albert prefer to the initial allocation X?
A firm uses two inputs to produce output: capital (𝐾) and labor for goods-production (𝐿𝑃). It produces output using one unit of 𝐿𝑃 and one unit of 𝐾, so its production function is
𝑞 = min{𝐿𝑃, 𝐾}
The firm does not buy capital. Instead it uses labor to produce its own capital equipment. Let the labor used for capital-production be 𝐿𝐾. The technology for producing capital is given by:
𝐾 = √𝐿𝐾
The final product is sold at a price of $9801. Each unit of labor costs $33 to hire, regardless of whether the worker is used for goods-production or for capital-production.
A firm’s production function is 𝑓(𝐿, 𝐾) = 4𝐿 + 10𝐾. Each unit of capital is paid 𝑟 = 100 per week and each unit of labor is paid 𝑤 = 25 per week. At these input prices, the firm’s optimal decision is to hire only labor and no capital.
A worker’s utility function is 𝑈(𝑤) = √𝑤, where 𝑤 is the wage that the worker is paid. With probability 23 the market wage will be 𝑤 = 1 and with probability 13 the market wage will be 𝑤 =
4. The worker can always find a job at the market wage.
a. Suppose, instead of paying the market wage, that a firm agrees to pay the worker a wage of 𝑤̅ for sure. What is the lowest wage 𝑤̅ for which the worker would agree to work for this firm?
b. Which results in lower expected labor costs for the firm – paying the market wage or paying the wage 𝑤̅ that you calculated in (a)? Show your work.
Asma allocates her income over many goods. She has normally-shaped indifference curves (i.e. the products are not perfect complements or perfect substitutes) and all goods are normal.
When peanuts cost $5, Asma buys 10 jars of peanuts. While the price of all other goods stays the same, the price of a jar of peanuts suddenly rises from $5 to $6.
