3. [2 + 4 + 6 + 7 = 19 pts] A rm has a production function given by: y = f(3313 $2: $3) = mlIl{\\/$1,2\\/E214\\/L'3} (i) Does this technology exhibit increasing, decreasing or constant returns to scale? (ii) Derive this rm's longrun cost function and show that it is C(i; yo) = 93 (w1+ % + Tg ). (iii) If the price of Y in a competitive market is p, derive this rm's supply and prot functions. (iv) The market for good Y is perfectly competitive and on the supply side there are 100 rms with the above cost function. 60 of them have the following price for the three inputs: ml 2 8,102 = 4, 203 = 16. The remaining 40 rms have the following input prices: wl = 14,1U2 = 8,1U3 = 64: On the demand side, the aggregate demand for good Y is given by y = 100 p, where p is the price of Y and y is the total demand. Derive the equilibrium price in this industry