**Problem 3:**

Write each production function given below in terms of output per person y ≡Y /L and capital per person k ≡ K/L. Plot these per person versions in a graph with y on the vertical axis and k on the horizontal axis. (You can assume Ā is a constant positive number).

(a) Y = ĀK 1/3 L2/3 and Y = ĀK 3/4 L1/4 (plot them on the same graph).

(b) Y = K.

(c) Y = K/ ĀL

(d) Y = K − ĀL

**Problem 5:**

Consider the following variation of the aggregate production function. Now firms must use oil M to produce output (in addition to labor and capital). The

price of a unit of oil is p

max Πf = AK α Lβ M γ − wL − rK − pM

(a) Find a first-order condition for the firm’s demand for oil.

(b) What must be true about the parameters α, β, and γ if this production function exhibits constant returns to scale?

(c) If the price of oil p rises, what would you expect to happen to carbon intensity (the ratio of oil per unit output: M/Y) in this economy? What happens to the revenue share of oil (the ratio of total oil payments to output: pM/Y)?

**Problem 6:**

Which of the following statements about the Solow model with population

growth are FALSE?

(a) An increase in the population growth rate lowers capital and output per capita in steady state.

(b) An increase in the saving rate always raises capital per capita in steady state.

(c) An increase in the saving rate always raises consumption per capita in steady state.

(d) An increase in TFP raises capital and output per capita

(e) None of the above

**Problem 7:**

Over the last 50 years in the US, GDP per person has grown at approximately

1% per year, while capital per person has been accumulating at around 0.5%

per year. Assume a capital share of 0.3. What is the growth rate of the Solow

residual?

**Problem 8:**

Consider the standard Solow model. The expression for output per worker and

the dynamics of capital per worker are given by the following expression:

y = Ak α

∆k = sy − δk

where δ > 0 is the depreciation rate of capital.

(a) Using a Solow diagram, what is the effect of an increase in productivity A on steady state capital? (label the axes and mark the initial and the final steady state level of capital)

(b) Find an algebraic expression for the steady state capital per worker.

(c) What happens to steady state output and consumption after a positive productivity shock? Justify your response.

(d) If the real wage equals the marginal product of labor, what is the growth rate of the real wage in steady state?

**Problem 11:**

In 2019, Maurizio Cattelan, an artist, put up an art in the form of a banana duct-taped on a wall in Miami at Art Basel. Each piece of this art sold for US$120000. This art came with a certificate from Cattelan, certifying the buyer purchased the art from him.

a) If only one piece of art was sold, what was the addition to US GDP?

(Assume Cattelan bought a banana for $1, and a piece of duct-tape for $2).

**Problem 12:**

Government policies should be designed to help maximize an economy’s GDP.

Is it True/False/Uncertain and Explain?

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