A consumer has $100 and would like to purchase food (F) and gas (G). Suppose their utility is given by:U (F, G) = F 0.8G0.2 .a) Find the consumer’s optimal consumption bundle give prices pF and pG for food and gas, respectively.b) Which good do you think the consumer likes more, and why? What the consumer might does with their budget. A consumer has $100 and would like to purchase food (F) and gas (G). Suppose their utilityis given byU(F, G) = F0.G2.a) Find the consumer's optimal consumption bundle give prices pr and pe for food andgas, respectively.b) Which good do you think the consumer likes more, and why? What theconsumer might does with their budget.

Given: U ( F,G ) = F 0.8 G 0.2 M= PF x F + PG x G 100 = PF x F + PGx G MUF= o.8 ( G / F ) 0.2 MUG = 0.2 ( F/G) 0.8 MUF / MUG = PF / PG 0.8 x ( G / F ) 0.2 / 0.2 ( F / G ) 0.8 = PF / PG 4 x G / F = PF / PG G = F x PF / 4 x PG puting the value of G in the above budget constraint we get, 100 = PF x F + PG x G 100 = PF x F + PG x ( Fx PF / 4 x PG) 100 = 4 PF x F + PF x F 100 = 5 PF x F PF x F = 20 so PG x G = 80 so optimal bundles for F = 20 / PF and for G = 80 / PG, Now if we consider PF = PG = 1 then G = 80 and F=20 so consumer will consume more units of G and less units of F. So at $100 cosumer can able to consume 80 units of G and 20 units of F. Budget constraint in this situation can be taken as 100 = PF x F + PG x G with PF = PG =1 , and G= 80 while F=20. If price is different from 1 then the units consumed may be different and the budget of the consumers may changed accordingly.