Suppose an economy produces two goods, X and Y, and the production function for the economy is given by Y = K^0.5X^0.5, where K is the stock of capital in the economy and X is the amount of labor employed. The current stock of capital is 100, and the current amount of labor employed is 25. The wage rate is $10 per unit of labor, and the rental rate of capital is $5 per unit of capital.

a) Calculate the marginal product of labor (MPL) and the marginal product of capital (MPK) at the current levels of labor and capital.

b) Is the production function exhibiting increasing, decreasing, or constant returns to scale at the current levels of labor and capital? Show your calculations.

c) Suppose the government increases the amount of labor employed to 30. Calculate the new output level and the new MPL.

d) Suppose the government introduces a new technology that increases the productivity of labor by 20%. The new production function is Y = K^0.5X^0.6. Calculate the new output level if the same amounts of labor and capital are employed as before.

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