6. USAEO Quantitative and Graphical Analysis

Multi Step Calculations — Quiz

Test your understanding of multi step calculations with 5 practice questions.

Practice Questions

Question 1

A firm produces a product with the following cost structure. The fixed cost is $500, and the variable cost per unit is $20. If the firm sells each unit for $50, how many units must the firm sell to break even?

Question 2

A monopolist faces a demand curve given by $P = 100 - 2Q$, where $P$ is the price and $Q$ is the quantity sold. The monopolist has a constant marginal cost of $20$ and no fixed costs. What is the profit-maximizing quantity?

Question 3

A firm operates in a perfectly competitive market and has a total cost function given by $TC = 100 + 5Q + 2Q^2$. If the market price is $45$, what is the profit-maximizing quantity for the firm?

Question 4

A consumer has a utility function $U(X, Y) = X^{0.5} Y^{0.5}$ and a budget of $100$. The price of good $X$ is $4$ and the price of good $Y$ is $1$. What is the optimal bundle of $X$ and $Y$ that maximizes the consumer’s utility?

Question 5

A firm faces the following production function: $Q = L^{0.5} K^{0.5}$, where $L$ is labor and $K$ is capital. The price of labor is $10$ per unit, and the price of capital is $40$ per unit. The firm wants to produce $100$ units of output. What is the cost-minimizing combination of $L$ and $K$?