ECON2011 Microeconomics Exam

Matt views conditioner (C) and shampoo (S) as perfect complements, using one squirt of conditioner for each squirt of shampoo. If shampoo costs $1 per squirt and conditioner costs $2 per squirt, and Matt has $9 to spend, how many squirts of each will he buy?

Geronimo's demand curve for apples is given by $a = \frac{p_bM}{p_a(p_a + p_b)}$, where $p_a$ is the price of apples, $p_b$ is the price of bananas, and $M$ is his income. Based on this information, are apples and bananas substitutes or complements? Explain.

Andre's demand for doughnuts is given by $Q = 5 - p$, Baby's by $Q = 6 - 2p$, and Cooper's by $Q = 4 - \frac{p}{2}$. Derive the market demand for doughnuts, taking into account the maximum price each consumer will pay.

Miquel and Jake's paper company uses the production function $Q = K^{1/2}L^{1/2}$ to produce reams of paper. They need to produce 10 reams of paper each week. If the price of capital (K) is $1 per unit and the price of labor (L) is also $1 per unit, how many units of each input should they use to minimize the cost of producing the 10 reams of paper? Explain.

A firm's total cost is given by $C(Q) = 15Q^2 + 8Q + 45$, where Q is the quantity of output. Find the average cost (AC) as a function of quantity.

A firm's total cost is given by $C(Q) = 15Q^2 + 8Q + 45$ where Q denotes the quantity of output. Find the marginal cost (MC) as a function of quantity.

A firm's total cost is $C(Q) = 15Q^2 + 8Q + 45$. For what quantities is the average cost greater than the marginal cost? Explain.

A firm's total cost is given by $C(Q) = 15Q^2 + 8Q + 45$ where Q denotes the quantity of output. Find the average variable cost (AVC) as a function of quantity.

Cardboard boxes are produced in a competitive market. A firm in this market has the cost function $C(q) = 3q^3 - 18q^2 + 40q + 50$, where q denotes the quantity of output. Find the fixed cost and the variable cost functions.

A firm's cost function is $C(q) = 3q^3 - 18q^2 + 40q + 50$. Find the marginal cost function.

A firm's cost function is given by $C(q) = 3q^3 - 18q^2 + 40q + 50$. For what prices will the profit-maximizing output be greater than zero? Explain.

Mariah consumes music downloads (x) and concert tickets (y). Her utility function is given by $U(x,y) = x^2 + 2y$. Find the equation for her indifference curve with $y$ as a function of $x$ when utility is equal to $U = 2$.

Mariah consumes music downloads (x) and concert tickets (y). Her utility function is given by $U(x,y) = x^2 + 2y$. Using the indifference curve from part (a) of the original question, is the marginal rate of substitution (MRS) diminishing as x increases?

Mariah consumes music downloads (x) and concert tickets (y). Her utility function is given by $U(x,y) = x^2 + 2y$. Do Mariah's preferences satisfy 'more is better'? Explain.

Mariah consumes music downloads (x) and concert tickets (y). Her utility function is given by $U(x,y) = x^2 + 2y$. What consumption bundle(s) are optimal when each good costs $1 per unit and Mariah's total income is $10?

Matt considers conditioner (C) and shampoo (S) as perfect complements and wants to consume one squirt of conditioner for each squirt of shampoo. Draw an indifference curve for (C, S) = (1,2). Be sure to label the axes and the point (1,2) on the indifference curve.

Geronimo has the demand curve for apples given by $a = \frac{p_bM}{p_a(p_a + p_b)}$, where $p_a$ is the price of apples, $p_b$ is the price of bananas, and $M$ is Geronimo's income. Based on this information, is an apple a normal or inferior good? Explain why.

Miquel and Jake run a paper company. Each week they need to produce 10 reams of paper. The production function for paper is given by $Q = K^{\frac{1}{2}}L^{\frac{1}{2}}$ where $Q$ is the number of reams of paper produced and $K$ and $L$ denote the number of inputs of capital and employed workers, respectively. Given these input prices, and the current production level $Q = 10$, what is the marginal cost of paper? Explain.

Miquel and Jake run a paper company. Each week they need to produce 10 reams of paper. The production function for paper is given by $Q = K^{\frac{1}{2}}L^{\frac{1}{2}}$ where $Q$ is the number of reams of paper produced and $K$ and $L$ denote the number of inputs of capital and employed workers, respectively. What is the average cost of paper at this level of production? Explain.