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Assume that you have the following open economy where C = 10 + 0.8(Y-T); I = 10; G = 10; T = 10 and imports and exports are given by IM = 0.3Y and X = 0.3Y* respectively where Y* is foreign output.
Then solve for the equilibrium output in the domestic economy given Y*. What is the multiplier effect for this open economy? What happens to Y and the trade balance over time if Y*'s economy grows faster than Y's economy. Assume the domestic government has a target level of output of 125 and the foreign country does not change G*, what increase in G is necessary to achieve the target output in the domestic economy? What would be the increase in G and T needed if the government wanted to keep a balanced
budget?

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Solution Preview

Total output is given by

Y = C + I + G + X - M

Plugging in the values from above we get

Y = 10 + 0.8(Y - 10) + 10 + 10 + 0.3Y* - 0.3Y
or Y = 10 + 0.8Y - 8 + 20 + 0.3Y* - 0.3Y
or Y = 0.5Y + 22 + 0.3Y* (1)
or Y - 0.5Y = 22 + 0.3Y*
or 0.5Y = 22 + 0.3Y*
or Y = 44 + 0.6Y*

Depending on what Y* is the value of Y can be determined using the above formula. Say for example Y* is 100, then Y = 44 + 0.6*100 = 104.

If we assume that in equilibrium Y = Y* then the equation can be solved as

Y = 44 + 0.6Y
or 0.4Y = 44
or Y = 110

The multiplier is given by

Multiplier = 1 / (1 - Slope of AE)

For a given Y* the slope of AE curve is the coefficient of Y on the right hand ...

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Calculating profit maximizing output level and price

Suppose a company has just introduced a new line of ceramic insulators for which it has received patent protection, effectively granting the company monopoly status in the industry. The company's revenue and cost relations are given as:

TR = $300Q - $0.001Q2

TC = $9,000,000 + $20Q + $0.0004Q2

where TR is total revenue, Q is output, and TC is total cost.

a) As a monopolist, calculate this firm's optimal output (Q) and price per unit (P).
b) Calculate the level of total profit at this output level and also the value of per unit profit at this output level.

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