# Econometrics, Regression, Tariffs

1) Consider a competitive market where inverse supply and demand are given by:

D: P = 160-2Q

S: P = 50+3Q

A) Solve for the equilibrium price.

B) If a $10 per unit tax is placed on this good, how much of the tax is paid by consumers? How much of the tax is paid by the firm? Show your work and explain in a sentence or two.

2) If you want to estimate the demand for a product, is it OK to regress Quantity on Price (and perhaps a few other variables) and interpret the results as the demand curve? Explain clearly.

3) We know that the minimum efficient scale of production varies widely across industries. How might the minimum efficient scale affect the level of competition in these industries? Explain in a few sentences.

4) The regression results below are for a company's sales. Quantity sold at various stores was regressed on the price charged at that store and average per capita income for the customers of that store. The results are reported below. (Assume the reported results are valid.)

SUMMARY OUTPUT

Regression Statistics

Multiple R 0.83

R Square 0.68

Adjusted R Square 0.68

Standard Error 1.25

Observations 100.00

ANOVA

Df SS MS F Significance F

Regression 2.00 324.81 162.40 104.40 6.52225E-25

Residual 97.00 150.89 1.56

Total 99.00 475.70

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%

Intercept 1.47 13.48 0.11 0.9136 -25.28 28.21

PRICE -0.50 0.05 -9.58 1.08078E-15 -0.60 -0.39

INCOME 2.04 0.22 9.39 2.79372E-15 1.61 2.47

A) Interpret the price and income coefficients. Explain clearly in a couple of sentences. Are the coefficients significant? Explain.

B) The standard error for the income coefficient was .22. If the standard error had been 1.5 would our estimate of 2.04 be significant? Explain.

5) In class we talked about why tariffs on imports usually reduce welfare. We also noted that the reason why tariffs are often used is that the government wants to protect or assist a particular domestic industry.

A) Explain why tariffs on imports reduce welfare and also use a graph to demonstrate your answer.

B) Instead of using a tariff to assist a domestic industry, suppose that the government used a production subsidy to assist firms. For instance the government might pay a per-unit subsidy to domestic firms for every unit produced domestically. (A subsidy is just a negative tax.) Why might the production subsidy result in higher welfare for the country than the tariff policy in part A? Explain clearly. Again, a graph might make your answer more clear.

6) Congress is considering legislation that will provide additional investment tax credits to businesses. Effectively, an investment tax credit reduces the cost to firms of using capital in production. Would you expect labor unions to lobby for or against such a bill? Explain clearly.

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#### Solution Preview

Please refer to the attachment.

1) Consider a competitive market where inverse supply and demand are given by:

D: P = 160-2Q (1)

S: P = 50+3Q (2)

A) Solve for the equilibrium price.

(1) - (2): 0 = 110 -5Q

solve for Q=110/5=22

then P= 50+3Q = 50+3*22 =116

B) If a $10 per unit tax is placed on this good, how much of the tax is paid by consumers? How much of the tax is paid by the firm? Show your work and explain in a sentence or two.

If a $10 per unit tax is placed on this good, it is like an increase in the unit cost of the supply side. Then we write the supply curve into: P = 50+3Q+10 = 60+3Q (3)

Now solve for the new equilibrium price

(1)- (3): 0 = 100 -5Q

solve for Q=100/5=20

then P= 60+3Q = 60+3*20 =120

At the equilibrium output level, the total tax revenue is T=t*Q =10*20=200

The tax each unit paid by consumers is the difference between the two prices:

tc=120-116= $4, then Tc=Q*tc =20*4= $80

The tax each unit paid by the firm is Tf=T-Tc = 200-80=$120

Deadweight Loss = Change in quantity*tax / 2 =(22-20)*10/2 = $10

2) If you want to estimate the demand for a product, is it OK to regress Quantity on Price (and perhaps a few other variables) and interpret the results as the demand curve? Explain clearly.

We cannot regress Quantity on Price and interpret the results as the demand curve, because there's Simultaneous Equation Bias if we do so.

In simultaneous systems of equations, endogenous variables are determined jointly rather than sequentially. Consider the following demand and supply functions for some product:

Qd = a1 + b1*P + c1*Y + d1*S + e1 demand

Qs = a2 + b2*P + c2*U + e2 supply

Q = Qd = Qs (market equilibrium)

The variables in this system are as follows:

QD : quantity demanded

QS : quantity supplied

Q : the observed quantity sold, which equates quantity supplied and quantity demanded in equilibrium

P : price per unit

Y : income

S : price of substitutes

U : unit cost

e1 : the random error term for the demand equation

e2 : the random error term for the supply equation

In this system, quantity demanded depends on price, income, and the price of substitutes. Consumers normally purchase more of a product when prices are lower and when income and the price of substitute goods are higher. Quantity supplied depends on price and the unit cost of production. Producers will supply more when price is high and when unit cost is low. The actual price and quantity sold are determined jointly by the values that equate demand and supply.

Since price and quantity are jointly endogenous variables, both structural equations are necessary to adequately describe the observed values. A critical assumption of OLS is that the regressors are uncorrelated with the residual. When current endogenous variables appear as regressors in other equations (endogenous variables depend on each other), this assumption is violated and the OLS parameter estimates are biased and inconsistent. Neither the demand nor supply equation can be estimated consistently by OLS.

3) We know that the minimum efficient scale of production varies widely across industries. How might the minimum efficient scale affect the level of competition in these industries? Explain in a few sentences.

(some brief introduction of minimum efficient scale, if you are familiar with the concept, you can skip this paragraph.)The minimum efficient scale (MES) is the output for a business in the long run where the internal economies of scale have been fully exploited. It corresponds to the lowest point on the long run average total cost ...

#### Solution Summary

Econometrics, Regression, Tariffs are emphasized.