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# Tax Rate, Tax Revenues, and Equilibrium Quantity of Capital

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1. In an economy, the supply curve of labour, S, is given by: S = -100 + 200W_n
Where W_n is the after-tax wage rate. Assume that the before-tax wage rate is fixed at 10.

a) Write a formula for tax revenues as a function of the tax rate, and sketch the function in a diagram with the tax rate, and sketch the function in a diagram with the tax rate on the horizontal axis and tax revenues on the vertical axis. (Hint: Note that W0 = (1 - t) 10, where t is the tax rate, and that tax revenues are the product of hours worked, the gross wage, and the tax rate.) Suppose that the government currently imposes a tax rate of 70 percent. Whast advice would you give?

b) Try this problem if you know some calculus: At what tax rate are tax revenues maximized in this economy?

2. Assume Canada is a small open economy such that the supply of capital is perfectly elastic at a net rate of return equal to 10 percent. Suppose the demand for capital in Canada is a downward sloping function of the net-of-tax rate of return (r_t) and economic depreciation. Depict the equilibrium quantity of capital in Canada and the user cost of capital (C) in the case where

a) There is no corporate taxation in Canada
b) There is corporate tax in Canada and the marginal investment is financed by the equity
c) There is a corporate tax in Canada and the marginal investment is financed by debt

https://brainmass.com/economics/supply-and-demand/tax-rate-tax-revenues-equilibrium-quantity-capital-532351

#### Solution Preview

Given that,
Supply curve of labor:

S=-100+200w_n
Or,

S=-100+200*100*(1-T)
Or,

Tax Revenue=S*w_n*T
Or,

Tax Revenue=(-100+200*10*(1-T))*10*(1-T)*T
Or,

Tax Revenue=(-100+2000*(1-T))*(10T-10T^2 )
Or,

Tax Revenue=(-100+2000-2000T)*(10T-10T^2 ...

#### Solution Summary

The expert examines tax rates, tax revenues and equilibrium quantity of capital.

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