consider in a small open economy

Consider a country, Home, that produces computers (C) and food (F) using capital (K) and labour (L). Both industries are perfectly competitive. The techniques of production in each industries are Leontief. As a result, unit factor requirements are fixed and given by: aKC=3,aKF=1, aLC=2, and aLF=4. Note: aij is the number of units of factor i required to produce a unit of goodj. a Which industry is capital intensive? How does the capitallabour ratio in each industry depend on the relative wage rw ? (5 points) b Suppose that the country has an aggregate endowment of 100 units of capital and 150 workers. Plot the country's production possibilities frontier (PPF). Laltel the axes, the intercepts, the slopes, and any kink in the PPF. (10 points) Autarky c Assume preferences are given by U(CC,CF)=CC21CF21. Add the indifference curve to the PPF and find the autarky production point (QF,QC). Solve for the relative demand for computers in terms of the relative price of computers. Find the autarky equilibrium value of the relative price PrPe. (10 points) d Solve for the labour and capital demand in each industry, i.e. (LC,LF,KC,KF), and the autarky equilibrium relative wage rw. Hint: the price of each good equals its marginal cost because of perfect competition. ( 10 points) Consider a country, Home, that produces computers (C) and food (F) using capital (K) and labour (L). Both industries are perfectly competitive. The techniques of production in each industries are Leontief. As a result, unit factor requirements are fixed and given by: aKC=3,aKF=1, aLC=2, and aLF=4. Note: aij is the number of units of factor i required to produce a unit of goodj. a Which industry is capital intensive? How does the capitallabour ratio in each industry depend on the relative wage rw ? (5 points) b Suppose that the country has an aggregate endowment of 100 units of capital and 150 workers. Plot the country's production possibilities frontier (PPF). Laltel the axes, the intercepts, the slopes, and any kink in the PPF. (10 points) Autarky c Assume preferences are given by U(CC,CF)=CC21CF21. Add the indifference curve to the PPF and find the autarky production point (QF,QC). Solve for the relative demand for computers in terms of the relative price of computers. Find the autarky equilibrium value of the relative price PrPe. (10 points) d Solve for the labour and capital demand in each industry, i.e. (LC,LF,KC,KF), and the autarky equilibrium relative wage rw. Hint: the price of each good equals its marginal cost because of perfect competition. ( 10 points)