In our models, we use symbols to represent economic variables, The actual symbol doesn't matter., All that matters is what the symbol is representing. Sometimes, we can tweak the models a little bit for them to look like the original model we already know. This question looks long but it isn't: you need very little math to solve it In the Solow model with technological and population growth, the produe- tion function is given by Yy = A (K (L) 7, where o (0,1). The law of motion of capit al is given by Kyp1 = (1-8) K +5Y5, where is the depreciation rate of capital and sis the savings rate. The growth rate of technology (A) is given by ~ and the growth rate of population (L) is given by n. On the Balanced Growth Path, income per capita grows as rate T 1= total income grows at rate n+ 1_7; and total capital grows at rate n+ 1_7; and the level of income per capita is given by 5 w= (497 (m) 1o Your goal in this question is to smartly transform the models below to look like the Solow model with a different not ation, and then simply apply the for- mulas for growth rates and level on the BGP. 1. Suppose we only eat hummus. To make hummus, we need blenders (B) and workers (W), The total amount of hummus (H) produced at time is given by: Hy = T:(B) (W), where T} is the level of technology, By is the number of blenders and W, is the number of workers at time f. Every period, we set aside a fraction a of hummus and transform it into blenders. Every vear, a fraction b of blenders breaks down. The growth rate of technology is g7 and the growth rate of number of workers is gw. You don't need to do any complicated math to answer this question. Just link this setting to the Solow model (a) Write the law of motion of blenders: By, = f(B;. Hy). (b) What is the growth rate of hummus per worker on the Balanced Growth Path? {c) What is the growth rate of total hummus and total blender on the BGP? {d) What is the level of hummus per worker on the BGP? 2, Suppose we're almost back in the Solow model. The law of motion is the same, just the production function is slightly different: Y: = (Ke)(ALy)' 7, Everything else is the same: L; grows at rate n, #A; grows at rate v, the savings rate is s and the depreciation rate is You need very little math to answer this question. Just link this seiting to the Selow model. (a) Create anew variable Ay such that the production function looks like Yy = Ay () (L)t ib] What is the growth rate of A,? {c) What is the growth rate of income per capita on the BGP7 (d) What is the level of income per capita on the BGP? 3. Solow meets Malthus: suppose that we modify the Solow model and we need land (X to produce output and the production function is: Y = A (K) (X)7 (L)' 77F where X is land and is fixed, and o + 3