ECON 0028: The Economics of Growth Term 1 (Fall 2022) ASSIGNMENT 3
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ECON 0028: The Economics of Growth
Term 1 (Fall 2022)
ASSIGNMENT 3
Due on (or before) November 27 (Sunday), 8pm
1. Classify the following goods on the rivalry – excludability spectrum (as on slide 15 in Week 5 lecture notes):
(a) a chicken
(b) a Coca-Cola recipe
(c) the Breaking Bad TV series
(d) tropical rainforest
(e) clean air
(f) a lighthouse guiding ships to the harbour
Then explain the role of the market and the government in providing these goods.
2. Consider the following production function: Y = 100 × (L - F)
where Y is output, L is labor input, F is a parameter that stands for a fixed amount of labor input required to produce the first unit of the good, akin to a research cost. Assume that Y = 0 whenever L < F . One unit of labor is paid wage w .
(a) Is this production function decreasing, constant, or increasing re- turns to scale? Justify your answer mathematically.
(b) How much does it cost, in terms of wages w, to produce 5 units of output?
(c) More generally, how much does it cost to produce Y units of out- put? Here you are asked to find the cost function C(Y). This function tells us the total cost of production of Y units of output. Plot this function (with output on the horizontal axis).
(d) Show that marginal cost, MC = , is constant (after the first unit is produced).
(e) Show that the average cost is declining in Y but it always remains above the MC. Plot both MC and AC.
(f) Profits of a firm are π = P .Y -C(Y). Explain what would happen to profits if P = MC .
3. In the Romer model we described in the lecture, people are employed in two sectors: the final goods producing sector and the R&D sector. How is the split of workers determined in equilibrium? (You are not required to derive the share of workers in the R&D sector – although of course you are welcome to, as this is a nice exercise using all the equilibrium conditions of the model. What you are required to do is to give a mathematical condition that has to hold in equilibrium, and explain the intuition behind it) . At some level this condition is clearly unrealistic. Speculate what is missing in the model to generate such a counterfactual prediction. Finally, explain the reasoning for why the share of labor in each sector has to be constant on the balanced growth path.
4. The key parameter of the Romer model is φ . Let’s think about how to estimate it, and in the process explore the difference between the rate of growth of technology outside of BGP (on the so called transition path) and on the BGP.
(a) As we have discussed in the lecture, the share of resources de- voted to R&D has been going up in the US and other advanced economies. In light of your answer to question 5, does this obser- vation suggest that these economies are on a BGP?
(b) For concreteness, assume that the number of researchers has been growing at about 3% per year, while TFP growth was constant at about 1% per year (so that the growth rate of – growth rate of the growth rate – is essentially zero). Start with the idea production function of the form
= θLA . Aφ − 1 .
Take logs and differentiate this expression, but do not equate the growth rate of researchers to population growth as of yet. Instead, plug in the numbers. What is the implied estimate of φ?
(c) Discuss what this estimate suggests about the balance of the standing on the shoulders and the fishing out effects.
(d) Assume that in the long-run, population growth will settle at 0.5% per year, and that advanced economies will converge towards a Balanced Growth Path we have studied in the lectures. What does your estimate of φ imply for the value of the long-run growth rate in the standard of living?
5. The Romer model predicts that when φ = 0 there will be zero growth in the very long run, irrespective of the population growth rate. True or false?
2023-04-28