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A consumer has the following utility function and income. 𝑈(𝑥, 𝑦) =1/2 * ln 𝑥 + 1/2 * ln y

Price of 𝑥 = Price of 𝑦 = 100. Income = 1000

Suppose that the consumer gets 2 redeemable coupons for a unit of x each, which cannot be sold.

I drew the budget constraint. However, I cannot find its equation to optimize it.

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You need to optimize as if the budget constraint was a regular straight line, taking in account the new maximum consumption of x. If the solution is unaffordable because it has too many units of y, then the optimum is as many as you can get of y, using all the coupons for x .

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