Question

Mr. Clarke likes to consume 7 cinders with 5 dinders. Let c denote cinders and d denote dinders.

a. Does Mr. Clarke consider cinders and dinders substitutes or complements?

b. Write down a utility function U(c, d) that represents Mr. Clarke’s preferences for cinders and dinders. In a graph with cinders on the horizontal axis and dinders on the vertical axis, draw an indifference curve that represents Mr. Clarke’s preferences. Be sure to label any important points within the graph.

c. The price of cinders and the price of dinders are pc and pd, respectively. Mr. Clarke has an income equal to Y. Solve for Mr. Clarke’s Marshallian demand functions for cinders and dinders.

d. Again, suppose the price of cinders and price and dinders are pc and pd, respectively. Solve for Mr. Clarke’s Hicksian demand functions for cinders AND dinders .

Answer 1

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c denotes under a'd' denotes dinders it's Consume Yanders with 5 dinders. ince the consumption is done together an example of complements, - 7 cinders consumed with scinders. So with I unders & dinders is consumed which implies : folos [d = $c] => { d = 56 ... o 1. So, utility can be written as : ſuz min {70,523..@. didinders) 7c 5+--| -- th U=35 it . >V=1 - >c cúnders) o | T c) Pc : price of unders ; Pa = pride of kinders Income & Y . Budget constraint :(cpetapa ayi substituting value of a from opet & pozy ①

[+ 5 ra ] - 71 1²7 1 . 7 pct 5 pd J marshellium demand for unders Marshallians demand 17 11 for dindern "pct 5pd J 7 l 7pct Spd { 7d, 5c } U= min substituting udure of cada u= min { 1 (su 1 spl), 5 (p port spa) } va ser per 35 Y u (1pc + 5 pd) zY - 35 now using shepard lemma. ay = he = 70 = he =b. 7 änder's I hickrian demand en het a hd => post cho I linders hicksi an demand T