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1.We are looking at an economy with 2 firms and 2 customers. Consumer no. 1 owns firm no.
1, which produces guns from oil. Its production function is b=2x. Customer 2 owns firm
no. 2. It produces butter out of oil with production function s=3x. Utility of customer 1 is
u (b , s )=b^4 s^6 and the utility of customer 2 is u (b , s )=10+0,5ln b+0,5 ln s .
(i) What is the price of guns, butter and oil?
(ii) How many guns, and how much butter does each customer use?
(iii) How much oil does each company use?2.
Look at an economy with 2 goods, x and y, and 1 production factor, z. Two types of people
are in the economy. Both have the utility function U (xi , yi )=min ( xi , yi ) , where xi and
yi are the consumption of customer i= α , β of x and y. Each customer α has a company that
produces good x and uses z as production factor. The profit function is Pα=(px)^2/4pz
. Each β
produces good y and uses z as production factor. The profit function is Pβ=(py)^2/pz
Look at an economy with 2 goods, x and y, and 1 production factor, z. Two types of people
are in the economy. Both have the utility function U (xi , yi )=min ( xi , yi ) , where xi and
yi are the consumption of customer i= α , β of x and y. Each customer α has a company that
produces good x and uses z as production factor. The profit function is Pα=(px)^2/4pz
. Each β
produces good y and uses z as production factor. The profit function is Pβ=(py)^2/pz
yi are the consumption of customer i= α , β of x and y. Each customer α has a company that
produces good x and uses z as production factor. The profit function is Pα=(px)^2/4pz
. Each β
produces good y and uses z as production factor. The profit function is Pβ=(py)^2/pz
produces good x and uses z as production factor. The profit function is Pα=(px)^2/4pz
. Each β
produces good y and uses z as production factor. The profit function is Pβ=(py)^2/pz
produces good y and uses z as production factor. The profit function is Pβ=(py)^2/pz
. We start
with no x and y but each r α and β owns 10 z. All producers and customers are price takers.
(i) Find the supply functions and demand for the production factor for α and β.
(ii) Find equilibrium prices.(i) What is the price of guns, butter and oil?
(ii) How many guns, and how much butter does each customer use?
(iii) How much oil does each company use?2.
Look at an economy with 2 goods, x and y, and 1 production factor, z. Two types of people
are in the economy. Both have the utility function U (xi , yi )=min ( xi , yi ) , where xi and
yi are the consumption of customer i= α , β of x and y. Each customer α has a company that
produces good x and uses z as production factor. The profit function is Pα=(px)^2/4pz
. Each β
produces good y and uses z as production factor. The profit function is Pβ=(py)^2/pz
Look at an economy with 2 goods, x and y, and 1 production factor, z. Two types of people
are in the economy. Both have the utility function U (xi , yi )=min ( xi , yi ) , where xi and
yi are the consumption of customer i= α , β of x and y. Each customer α has a company that
produces good x and uses z as production factor. The profit function is Pα=(px)^2/4pz
. Each β
produces good y and uses z as production factor. The profit function is Pβ=(py)^2/pz
yi are the consumption of customer i= α , β of x and y. Each customer α has a company that
produces good x and uses z as production factor. The profit function is Pα=(px)^2/4pz
. Each β
produces good y and uses z as production factor. The profit function is Pβ=(py)^2/pz
produces good x and uses z as production factor. The profit function is Pα=(px)^2/4pz
. Each β
produces good y and uses z as production factor. The profit function is Pβ=(py)^2/pz
produces good y and uses z as production factor. The profit function is Pβ=(py)^2/pz
. We start
with no x and y but each r α and β owns 10 z. All producers and customers are price takers.
(i) Find the supply functions and demand for the production factor for α and β.
(ii) Find equilibrium prices.
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