Answer the economics questions

A car manufacturer runs tests to investigate the fuel consumption of cars using a newly developed fuel additive. Sixteen cars of the same make and age are used, eight with the new additive and eight as controls. The results, in miles per gallon over a test track under regulated conditions, are as follows: Control 22.0 32.2 30.4 28.0 26.5 25.5 29.6 22.2 Additive 31.4 29.9 33.2 34.4 32.0 23.7 26.] 30.3 If ,an is the mean number of miles per gallon achieved by cars in the control group, and ,u,' is the mean number of miles per gallon achieved by cars in the group with fuel additive, test: {:1} H:,uA,uc=0 vs Elnab\" (ii) H:,uA,uc= vs H]:,uA,u5: The following table shows the total utility that Peter receives from consuming various quantities of Good X and Good Y. Units of Total utility Marginal utility Total utility Marginal utility good from units of from each unit from units of from each unit consumed Good X of Good X Good Y of Good Y consumed consumed consumed consumed 10 12 2 18 22 3 25 30 4 30 36 5 34 40 6 37 43 (i) Complete the columns for the marginal utility of Good X and the marginal utility of Good Y. (ii) If Good X costs f2 and Good Y costs f4, list the possible combinations of goods that would satisfy the condition for the optimum combination of goods consumed and calculate the total utility of each combination. (iii) Assuming that Peter has f16 to spend on the two goods (and that there are no other goods available), identify the combination of Good X and Good Y that he will consume. (iv) If Peter's income now increases to f20, determine the combination of goods he will now buy