Consider an economy with 100 identical households and 100 identical firms. Each household is endowed with one unit of time. Half of the households are endowed with equal shares of firm, while the rest are endowed with no firm shares. A householdís utility is u (x; r) = 2 ln(x*r^2) , where x is consumption of goods, r = 1- l is leisure time and l is the householdís labour supply. Each firm hires households to produce goods according to technology y = L^1/2, where L denotes the labour input. Goods price p, wage rate w, and dividend income are all taken as given. Normalize w = 1. Do the following: (a) Derive the Marshallian demands, x (p, D) and r (p,D), where D is dividend. (b) Derive the firmís input demand function L (p) and profit function pi(p). (c) List all the market-clearing conditions.
Consider an economy with 100 identical households and 100
identical firms. Each household is endowed with one unit of time. Half of the households are endowed with equal shares of firm, while the rest are
endowed with no firm shares. A householdís utility is u (x; r) = 2 ln(x*r^2) ,
where x is consumption of goods, r = 1- l is leisure time and l is the
householdís labour supply. Each firm hires households to produce goods
according to technology y = L^1/2, where L denotes the labour input. Goods
w = 1. Do the following: (a) Derive the Marshallian demands, x (p, D) and
r (p,D), where D is dividend. (b) Derive the firmís input
L (p) and profit function pi(p). (c) List all the market-clearing conditions.
(d) Calculate the
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