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8. In the economy of the Kingdom of Monomania, households spend their incomes on domestically produced goods, Cd, and imported goods, M. This spending is observed to follow the relationship Cd+M=aY (1) where a is a parameter and Y = households' income. Imports are observed to be related to household consumption by the relationship M = mCd (where m is a parameter) (2) The equilibrium condition for this economy is that aggregate output, Y, must equal the demand for output for domestic consumption, Cd, and domestic investment, .-', plus demand for exports by foreigners, X. Therefore the equilibrium condition is Y=Cd+I+X (3) (where land X are assumed to be exogenous). Note that household income is necessarily equal to output because households earn their incomes (wages, salaries and prots) by producing output. (a) Show that, after suitable rearrangement, the set of simultaneous equations 1 to 3 above can be written as Ax = b, where A is a matrix containing the parameters of the model (a and m); x is a vector containing the endogenous variables (Y, Cd and M) and b is a vector containing the exogenous variables (l and X). (b) By calculating A", nd the equilibrium values of the endogenous variables in terms of the values of the parameters and exogenous variables. (0) Using your answer to (b), nd the equilibrium values of the endogenous variables when a = 0.75, m = 0.25,and l+ X =1000. Check your answer by solving the model by simultaneous equation methods. (C!) Use your answer to (b) to calculate the effect on Y, C, and M of a small increase in each of the exogenous variables, it or X. (e) What is the relationship between exports and imports in this model