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# problem2micro - 2 There are two types of consumers A and 3...

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Unformatted text preview: 2- There are two types of consumers: A and 3. They have the following utility Emotions _ 0.5 0.5 UAWMJM) — \$1A'32A _ 0.4 as UB(313;\$23) — mlB'mEB where :31 A [3:13) denotes the quantity of good 1 consumer of type A {B} is consuming and mm (3:23) denotes the quantity of good 2 consumer of type A (B) is consuming. Assume that the budget constraint is satisﬁed and let IA and I3 he the income level of type A and B? respectively. (a) {5 marks) Depict the indifference curve of consumer A for the utility level of 36 in a [m1A3m2A)— diagram. (h) {5 marks) Depict the indiﬁ'erence curve of consumer B for the utility level of 12 in a [.1113] 3:33)— diagram- (c) f 16‘ moms) Derive the demand curves each type of consumer is consuming in the optimum for each good :31} and may and j = A, B- (d) {5 marks} Suppose there are 1ﬂﬂ households of type A and B- Derive the aggregate demand curve for good Xi} and X21) . [Hint X? = lﬂﬂmm + Mlle-13}- Suppose there are two types of ﬁrms1 hoth using labour, I, and capital1 k, as input. The production function for a ﬁrm of type 1 is 3:1 2 issrlfﬂezfa; and for a ﬁrm of type 2 m2 = srlr’ﬁklw’“- (e) {1E3 moms) Derive for each ﬁrm the optimal demand for labour and capital. In your analysis? denote the hourly wage rate by a} and the price per unit of capital by r- (f) {5 marks) Assume further that there are lﬂﬂ ﬁrms of type 1 and IUD ﬁrms of type 2. Derive the aggregate demand for labour and capital- (g) {5 marks) A consumer of type A is endowed with El] units of labour and no capital. In contrast] a consumer of type B is endowed with ID units of labour and BI] units of capital- 1‘What is the economy wide supply of labour and capital? (h) {5 marks} Based on your answer to part g] and h} derive equilib- rium conditions for the labour market and capital market. (i) {5 marks) Derive the market supply curves for good 1 and good 2 ' 5 marks 1What are the an 1 uals—demand conditions for ood (J) I” PPr-eq s 1 and good 2 mac'rkets'iI (k) {3 marks) Illustrate the equilibrium conditions graphically. (1} (It? mart-.3) How would you ﬁnd the general equilibrium for this economy? What is the signiﬁcance of ‘Walras‘ Law in this case? ...
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