Match the Cobb-Douglas production function below with a graph in the given figure and a statement.

$$F(L, K)=L^{0.25} K^{0.25}$$

Match the statement below with a graph in the given figure.

Quadrupling each input doubles output.

Total sales, Q, of a product are a function of its price and the amount spent on advertising. The figure shows a contour diagram for total sales. Which axis corresponds to the price of the product and which to the amount spent on advertising? Explain.

Decide if the statement must be true, might be true, or could not be true. The function $z=f(x, y)$ is defined everywhere.

The level curves corresponding to $z=1$ and $z=-1$ cross at the origin.

Decide if the statement must be true, might betrue, or could be true. The function $z=f(x, y)$ is defined everywhere.

If $z=e^{-\left(x^2+y^2\right)}$, there is a level curve for every value of $z$.

Decide if the statement must be true, might betrue, or could be true. The function $z=f(x, y)$ is defined everywhere.

If $z=e^{-\left(x^2+y^2\right)}$, there is a level curve through every point $(x, y)$

Figure is a contour diagram of the monthly payment on a 5-year car loan as a function of the interest rate and the amount you borrow. The interest rate is 8% and you borrow $6000 for a used car. (a) What is your monthly payment? (b) If interest rates drop to 6%, how much more can you borrow without increasing your monthly payment? (c) Make a table of how much you can borrow, without increasing your monthly payment, as a function of the interest rate.

The figure is a contour diagram of the monthly payment on a 5-year car loan as a function of the interest rate and the amount you borrow. The interest rate is 13% and you borrow $6000 for a used car.

If interest rates drop to 11%, how much more can you borrow without increasing your monthly payment?

Figure $12.59$ is a contour diagram of the monthly payment on a $5$-year car loan as a function of the interest rate and the amount you borrow. The interest rate is $13 \%$ and you borrow $\$ 6000$ for a used car.

(a) What is your monthly payment?

Figure shows a contour map of a hill with two paths, A and B. (a) On which path, $A$ or $B$, will you have to climb more steeply? (b) On which path, $A$ or $B$, will you probably have a better view of the surrounding countryside? (Assume trees do not block your view.) (c) Alongside which path is there more likely to be a stream?

The figure shows a contour map of a hill with two paths, A and B.

On which path, A or B, will you have to climb more steeply?

Match the given contour diagrams with the surfaces. Give reasons for your choice.

A manufacturer estimates the Cobb-Douglas production function to be given by

$$f(x, y)=100 x^{0.75} y^{0.25} \text {. }$$

Estimate the production levels when x=1500 and y=1000.

Deduce that the Cobb-Douglas production function is $P=1.01 L^{0.75} K^{0.25}$.