This problem asks you to analyze the is-lm model algebraically. suppose consumption is a linear function of disposable income c(y-t) = a + b(y-t) where z>0 and 01. the parameter b is the marginal propensity to consume, and the parameter a is a constant sometimes called autonomous consumption. suppose also that investment is a linear function of the interest rate: i(r) =c - dr where c>0 and d>0. the parameter d measures the sensitivity of investment to the interest rate, and the parameter c is a constant sometimes called autonomous investment. a solve for y as a function of r, the exogenous variables g and t, and the model's parameters a, b, c and

d.