6. USAEO Quantitative and Graphical Analysis

Quantitative Scenario Analysis — Quiz

Test your understanding of quantitative scenario analysis with 5 practice questions.

Practice Questions

Question 1

A firm operates in a perfectly competitive market. Its total cost function is given by $TC(Q) = 150 + 10Q + 0.5Q^2$. If the market price is $P = 35$, how many units should the firm produce to maximize profit?

Question 2

A monopolist faces the demand curve $P = 100 - 2Q$ and has a total cost function $TC(Q) = 20Q + 150$. What is the profit-maximizing quantity for the monopolist?

Question 3

An economy consists of two goods: X and Y. The price of good X is $P_X = 4$ and the price of good Y is $P_Y = 2$. A consumer has a budget of $B = 100$. The utility function is $U(X,Y) = X^2 Y$. What combination of $X$ and $Y$ maximizes the consumer’s utility?

Question 4

A firm’s production function is given by $Q = L^{0.5} K^{0.5}$, where $L$ is labor and $K$ is capital. The firm faces a wage rate of $w = 10$ and a rental rate of capital $r = 20$. If the firm wants to produce 100 units of output, what is the cost-minimizing combination of $L$ and $K$?

Question 5

Suppose an economy is described by the following IS-LM model. The IS curve is given by $Y = 500 - 20r$, and the LM curve is given by $Y = 100 + 10r$. What is the equilibrium interest rate $r$?