What is the IS curve?

(7 points) Assume that the consumption function is given by C = 200 + 0.75(Y -T). Govern- ment purchases and taxes are both 100. Planned investment is derived as follows: there are many ideas, whose cost of implementation are all 3. Ideas are indexed by j > 0. Idea j produces j units of return next year. Index j follows an exponential distribution on (0, co) with density 100e-i, j > 0. Derive the IS curve