Equilibrium price ratio
Find the equilibrium price ratio and allocations for the following utility functions and endowments
1. U A(x, y) = x 1/3y 2/3 U B(x, y) = x 2/3y 1/3 e A x = 100, eA y = 100, eB x = 100, eB y = 100
2. Same as 1 except both consumers increase endowment of x to 200 (e A x = e B x = 200)
3. Same as 1 except both consumers increase endowment of y to 200 (e A y = e B y = 200)
4. Same as 1 except consumer A’s endowment of both goods increases to 200 (e A x = e A y = 200)
5. Same as 1 except consumer A’s endowment of both goods increases to 200 (e B x = e B y = 200)
6. Compare the price ratios you got in 2-5 to the price in 1. Come up with an economic intuition for why they changed in the direction they did.
7. U A(x, y) = 2x + y U B(x, y) = 2x + 5y e A x = 100, eA y = 100, eB x = 100, eB y = 100 (hint: each consumer will only consume one type of good in equilibrium. Why? Can you guess which good each consumer will consume?)
8. U A(x, y) = x 1/2y 1/2 U B(x, y) = x 1/4y 3/4 U C(x, y) = x 3/4y 1/4 e A x = 100, eA y = 100, eB x = 100, eB y = 100, eC x = 100, eC y = 100 (hint: There are three consumers in this economy, but the same definitions hold. All consumers must be maximizing utility and markets must clear.)
Sample Solution
McGee and Daly (2007) discussed that there is evidence that incidental teaching and stimulus-fading techniques can enhance autistic children’s communication in a socially meaningful way. A study was done that evaluated peer incidental teaching as a way to increase peer interactions by children with ASD (McGee, Almeida, Sulzer-Azaroff, and Feldman, 1992). The study gave a typical child something to say that would elicit a response from their peer with ASD (McGee et al., 1992). Three typical preschoolers were trained and paired with three children with ASD in a natural free play environment (McGee et al., 1992). There was adult supervision that was systematically faded throughout the sessions, which resulted in increase reciprocal interactions among the peers (McGee et al., 1992). Evidence showed that peer incidental teaching was effective in improving and enhancing reciprocal interactions among children with autism and their typical peers (McGee et al., 1992).