1- Solve the partial derivative of the following functions with respect to each independent variable:

2- Does any of the following production functions exhibit constant returns to scale?

3-Please see if these statements are true, False or uncertain, Provide the right explanation for that:

a-. Imported goods will change the CPI of a given country, and change the value of real GDP

b- A decrease in capital stock will increase marginal productivity of capital.

c- More labor will increase the Marginal productivity of capital.

d- If real interest rate is greater than nominal exchange this Imply that borrowers are happy.

4- Imagine AD and AS represent the main forces driving the business cycle in a country. You have been chosen as Treasury Secretary to take critical decisions. Your country has been going through difficult economic times, as people are unhappy with their level of income and employment. You decide to implement a policy to (Stimulate) the economy.

a- what is the equilibrium state of the economy, and how is that related to the potential GDP? Please write the equilibrium equation down. If, You decided to increase G, how does this policy affect the AD?

b- Sketch the above effect/effects on a graph. Explain.

c- Two years after the increase in G, you observe that prices in the economy had gone up. However, you do not have any data on other
variables such as Y, C, and I. You hire an economist to figure out the effect of prices on Y, C, and Investments, and to see why prices went up at the first place. What do you expect she will tell you? Did these variables go up, down or stay the same? Please explain your points.

d- Has the policy been beneficial for your country? In particular, what has happened to consumption?